This is the fourth in a series of five blog posts that we will be publishing this week highlighting challenging exponent questions!
This week on Beat The GMAT, Veritas Prep’s authors will each day contribute a difficult exponent-related challenge problem, with a solution to follow the next day. Before you begin, you may want to consider this as a way to crack the exponent code; nearly all exponent-based problems can be solved using a combination of these three guiding exponent principles:
- Exponent rules are almost all related to multiplication and division with virtually no rules that directly apply to addition and subtraction. When facing exponent problems, look for opportunities to factor and multiply to put yourself in a position to use your multiplication-heavy exponent expertise.
- Most exponent rules require you to have common bases in order to apply them, so look to break down bases into prime factors so that you have common bases with which to work.
- Exponents are very pattern-driven, so when large numbers are present you can often establish a rule using small numbers and then extrapolate it to the larger ones.
Yesterday’s Challenge Question and Solution
If you haven’t don’t so already, try out yesterday’s problem first before reviewing the solution.
C. When working with exponents, you should try to find common (typically prime) bases and multiply. First to multiply, you can factor a out of each additive term within the parentheses to get: . Then, perform the addition within the parentheses to get: .
You can break down to be , which is , and then you have common prime terms for each exponent: .
Multiplying out the equation , you get: and , which can be simplified to .
This can be expressed as , and the correct answer is C.
Today’s Challenge Question
What is the tens digit of ?